Lower Percentile Estimation of Accelerated Life Tests with Nonconstant Scale Parameter

Abstract

Lower percentiles of product lifetime are useful for engineers to understand product failure, and avoiding costly product failure claims. This paper proposes a percentile re-parameterization model to help reliability engineers obtain a better lower percentile estimation of accelerated life tests under Weibull distribution. A log transformation is made with the Weibull distribution to a smallest extreme value distribution. The location parameter of the smallest extreme value distribution is re-parameterized by a particular 100pth percentile, and the scale parameter is assumed to be nonconstant. Maximum likelihood estimates of the model parameters are derived. The confidence intervals of the percentiles are constructed based on the parametric and nonparametric bootstrap method. An illustrative example and a simulation study are presented to show the appropriateness of the method. The simulation results show that the re-parameterization model performs better compared with the traditional model in the estimation of lower percentiles, in terms of Relative Bias and Relative Root Mean Squared Error.

QUALITY PAPERA new rapid and robust multi-factorial screening for low-percentile use-rate accelerated reliability analysis

“…It is advantageous then to make decisions at low percentiles that match product failure tolerances. Such action could aid in protecting against customer claims (Chen et al , 2016; Lv et al , 2017a). We refrain from completing a full contemporary review on the subject since this has currently been accomplished by Wang et al (2017).…”

“…Reliability engineers usually resort to accelerated use-rate testing to rapidly ensnare new or improved product life information (Collins et al , 2013; Meeker and Escobar, 1998; Nelson, 1990). To speed-up further the decision making process, one smart strategy is to force the extraction of information at low percentiles of life-time data (Lv et al , 2017a). This will require a robust prediction before triggering the expedition of a beneficial decision.…”

Estimating confidence lower bounds of Weibull lower percentiles with small samples in material reliability analysis

“…Lv ve diğ. [26], Weibull alt yüzdeliklerin tahmini için yüzdelik yeniden parametreleme modelini önermişlerdir.…”

Reliability analysis of Weibull multicomponent system with stress‐dependent parameters from accelerated life data

“…However, such conventional life‐stress model assumption does not work satisfactorily and low‐accuracy extrapolation even misleading results may be obtained in many applicative examples. Such motivated real life data analysis appears for dielectrics data from an electric‐field accelerating experiment (e.g., Li et al 2 and Hiergeist 3 ), fatigue data of 304 6061‐T6 aluminum coupons failure data under cyclic stress test (e.g., D'Anna et al 4 ), polyethylene terephthalate (PET) film data in electrical insulation under voltage‐accelerated test (e.g., Lv et al 5 ), among others. From this point of perspective, in order to improve the inferential accuracy of extrapolation, various studies of ALTs for real life data are discussed by many authors, where some general life‐stress relationships are assumed with multiple stress‐affected parameters in probability model that show superior performance than classical sole stress‐affected parameter assumption.…”